Problem: Which of the following numbers is a multiple of 2? ${45,87,89,114,117}$
The multiples of $2$ are $2$ $4$ $6$ $8$ ..... In general, any number that leaves no remainder when divided by $2$ is considered a multiple of $2$ We can start by dividing each of our answer choices by $2$ $45 \div 2 = 22\text{ R }1$ $87 \div 2 = 43\text{ R }1$ $89 \div 2 = 44\text{ R }1$ $114 \div 2 = 57$ $117 \div 2 = 58\text{ R }1$ The only answer choice that leaves no remainder after the division is $114$ $ 57$ $2$ $114$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $2$ are contained within the prime factors of $114$ $114 = 2\times3\times19 2 = 2$ Therefore the only multiple of $2$ out of our choices is $114$. We can say that $114$ is divisible by $2$.